Yu-Kun Lai

Fast mesh segmentation using random walks

3D mesh models are now widely available for use in various applications. The demand for automatic model analysis and understanding is ever increasing. Mesh segmentation is an important step towards model understanding, and acts as a useful tool for different mesh processing applications, e.g. reverse engineering and modeling by example. We extend a random walk method used previously for image segmentation to give algorithms for both interactive and automatic mesh segmentation. This method is extremely efficient, and scales almost linearly with increasing number of faces. For models of moderate size, interactive performance is achieved with commodity PCs. It is easy-to-implement, robust to noise in the mesh, and yields results suitable for downstream applications for both graphical and engineering models.

Robust Feature Classification and Editing

Sharp edges, ridges, valleys, and prongs are critical for the appearance and an accurate representation of a 3D model. In this paper, we propose a novel approach that deals with the global shape of features in a robust way. Based on a remeshing algorithm which delivers an isotropic mesh in a feature-sensitive metric, features are recognized on multiple scales via integral invariants of local neighborhoods. Morphological and smoothing operations are then used for feature region extraction and classification into basic types such as ridges, valleys, and prongs. The resulting representation of feature regions is further used for feature-specific editing operations

Rapid and effective segmentation of 3D models using random walks

3D models are now widely available for use in various applications. The demand for automatic model analysis and understanding is ever increasing. Model segmentation is an important step towards model understanding, and acts as a useful tool for different model processing applications, e.g. reverse engineering and modeling by example. We extend a random walk method used previously for image segmentation to give algorithms for both interactive and automatic model segmentation. This method is extremely efficient, and scales almost linearly with the number of faces, and the number of regions. For models of moderate size, interactive performance is achieved with commodity PCs. We demonstrate that this method can be applied to both triangle meshes and point cloud data. It is easy-to-implement, robust to noise in the model, and yields results suitable for downstream applications for both graphical and engineering models.

Robust principal curvatures on multiple scales

Geometry processing algorithms often require the robust extraction of curvature information. We propose to achieve this with principal component analysis (PCA) of local neighborhoods, defined via spherical kernels centered on the given surface Φ Intersection of a kernel ball Br or its boundary sphere Sr with the volume bounded by Φ leads to the so-called ball and sphere neighborhoods. Information obtained by PCA of these neighborhoods turns out to be more robust than PCA of the patch neighborhood Br∩Φ previously used. The relation of the quantities computed by PCA with the principal curvatures of Φ is revealed by an asymptotic analysis as the kernel radius r tends to zero. This also allows us to define principal curvatures at scale r in a way which is consistent with the classical setting. The advantages of the new approach are discussed in a comparison with results obtained by normal cycles and local fitting; whereas the former method somewhat lacks in robustness, the latter does not achieve a consistent behavior at features on coarse scales. As to applications, we address computing principal curves and feature extraction on multiple scales.

Automatic and topology-preserving gradient mesh generation for image vectorization

Gradient mesh vector graphics representation, used in commercial software, is a regular grid with specified position and color, and their gradients, at each grid point. Gradient meshes can compactly represent smoothly changing data, and are typically used for single objects. This paper advances the state of the art for gradient meshes in several significant ways. Firstly, we introduce a topology-preserving gradient mesh representation which allows an arbitrary number of holes. This is important, as objects in images often have holes, either due to occlusion, or their 3D structure. Secondly, our algorithm uses the concept of image manifolds, adapting surface parameterization and fitting techniques to generate the gradient mesh in a fully automatic manner. Existing gradient-mesh algorithms require manual interaction to guide grid construction, and to cut objects with holes into disk-like regions. Our new algorithm is empirically at least 10 times faster than previous approaches. Furthermore, image segmentation can be used with our new algorithm to provide automatic gradient mesh generation for a whole image. Finally, fitting errors can be simply controlled to balance quality with storage.

Metric-Driven RoSy Field Design and Remeshing

Designing rotational symmetry fields on surfaces is an important task for a wide range of graphics applications. This work introduces a rigorous and practical approach for automatic N-RoSy field design on arbitrary surfaces with user-defined field topologies. The user has full control of the number, positions, and indexes of the singularities (as long as they are compatible with necessary global constraints), the turning numbers of the loops, and is able to edit the field interactively. We formulate N-RoSy field construction as designing a Riemannian metric such that the holonomy along any loop is compatible with the local symmetry of N-RoSy fields. We prove the compatibility condition using discrete parallel transport. The complexity of N-RoSy field design is caused by curvatures. In our work, we propose to simplify the Riemannian metric to make it flat almost everywhere. This approach greatly simplifies the process and improves the flexibility such that it can design N-RoSy fields with single singularity and mixed-RoSy fields. This approach can also be generalized to construct regular remeshing on surfaces. To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sketching and geometry remeshing. Furthermore, based on our remeshing results with high global symmetry, we generate Celtic knots on surfaces directly.

Principal curvatures from the integral invariant viewpoint

The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighborhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asymptotic analysis of the moments of inertia and the principal directions which are used in this approach. We also address implementation and, briefly, robustness issues and applications.

Geometric texture synthesis and transfer via geometry images

In this paper, we present an automatic method which can transfer geometric textures from one object to another, and can apply a manually designed geometric texture to a model. Our method is based on geometry images as introduced by Gu et al. The key ideas in this method involve geometric texture extraction, boundary consistent texture synthesis, discretized orientation and scaling, and reconstruction of synthesized geometry. Compared to other methods, our approach is efficient and easy-to-implement, and produces results of high quality.

An incremental approach to feature aligned quad dominant remeshing

In this paper we present a new algorithm which turns an unstructured triangle mesh into a quad-dominant mesh with edges aligned to the principal directions of the underlying geometry. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to the principal directions. The quad-dominant mesh is eventually obtained by dropping the not-aligned diagonals from the triangle mesh. A post-processing stage is introduced to further improve the results. The major advantage of our algorithm is its conceptual simplicity since it is merely based on elementary mesh operations such as edge collapse, flip, and split. The resulting meshes exhibit a very good alignment to surface features and rather uniform distribution of mesh vertices. This makes them very well-suited, e.g., as Catmull-Clark Subdivision control meshes.

Surface fitting based on a feature sensitive parametrization

Most approaches to least squares fitting of a B-spline surface to measurement data require a parametrization of the data point set and the choice of suitable knot vectors. We propose to use uniform knots in connection with a feature sensitive parametrization. This parametrization allocates more parameter space to highly curved feature regions and thus automatically provides more control points where they are needed.